Final answer:
The deer takes approximately 0.277 seconds to reach its maximum height.
Step-by-step explanation:
To find the time it takes for the deer to reach its maximum height, we need to analyze its vertical motion.
The initial vertical velocity of the deer is given by the equation Vyi = V * sin(θ), where V is the initial velocity and θ is the angle.
In this case, Vyi = 3.75 m/s * sin(46.3°) = 2.716 m/s.
The time it takes to reach maximum height can be found using the equation t = Vyi / g, where g is the acceleration due to gravity.
Assuming g is 9.8 m/s², t = 2.716 m/s / 9.8 m/s² = 0.277 seconds.
Therefore, it takes approximately 0.277 seconds for the deer to reach its maximum height.